Corresponding to the increased integration of semiconductor devices, there are considerable problems regarding the decreased reliability of metal interconnects connecting the microscopic elements that accompany such miniaturization. Electromigration (EM) is pointed to as the main cause of failures in the metal interconnects. EM is the phenomenon where atoms of metal structuring an interconnect migrate due to high density current. In places where atomic flux is uneven because of EM, localized loss and accumulation of atoms develops and is referred to as atomic flux divergence. This loss and accumulation of atoms leads to the occurrence of voids (clumps of vacancies) and hillocks (clumps of metallic atoms), respectively. As voids develop corresponding to stressing electric current and the cross-sectional area of the interconnect decreases, current density increases to cause localized increases in temperature and even melting. In order to ensure interconnect reliability, it is vital that EM damage, such as the formation of voids or hillocks, and failure, be accurately predicted.
Until now, the effects of two-dimensional current density and temperature distributions on the formation of voids has been studied, and it has become clear that the current density, current density gradient, temperature, temperature gradient of the interconnect as well as the material properties of the material forming the interconnect are the factors of void formation.
The key to EM damage prediction is the accurate and easy determination of how much atomic flux divergence is occurring. Until now, the atomic flux divergence has been formulated considering one-dimensional temperature distributions, and based on the failure prediction has been attempted for straight shaped polycrystalline interconnects. However, since the constitution of the crystal grains of an interconnect, or in other words the interconnect microstructure, is not taken into consideration, its suitability has been limited.
In addition, the study of atomic flux divergence in view of the two-dimensional distribution of current density and temperature for so-called ‘bamboo’ interconnects, which are strings of simple crystals, has not yet been carried out.
Interconnect lifetime estimation is performed by extrapolating the results of breakage testing under EM accelerated test conditions for normal conditions of use. For such extrapolation, empirical methods are used; however, problems such as differences in estimation results develop due to the selection of accelerated test conditions and interconnect layouts, and there has yet to be a universal lifetime estimation method.